In my previous post on the concept of physicalism I wrote:
Physicalism, as understood in my book (and the definition is laid out clearly) is committed to three fundamental doctrines. 1) Physics is mechanistic at the most basic level of analysis. Whetever is happening to the basic stuff of the universe is fully determined by the laws of physics, the initial conditions, and perhaps a quantum chance factor. 2) Physics is closed. No physical event has a nonphysical cause. 3) Whatever exists in space and time that is not physical supervenes on the physical. Given the state of the physical, whatever states that are not physical must be the way they are and not some other way. So, for example, we can describe the braking system of a car in physical terms that does not mention the capability of stopping a car, but given the state of the physical, the braking capacities of the system are guaranteed to be there. Nothing in this definition requires reductionism, and this definition should encompass all forms of materialism, whether they are eliminative, reductive, or non-reductive. Is this definition of physicalism in any way a straw man?
But now that I go back and look at my book, I find that I wrote the following: (CSLDI, pp. 52-53).
1. The physical level is to be understood mechanistically, sucht aht purposive explanations must be further explained in terms of a non-purposive substratum. This will be called the mechanism thesis.
2. The physical order is causally closed. No nonphysical causes operate on the physical level. The physical is a comprehensive system of events that is not affect by anything that is not itself physical. (I really should have said physical in the final analysis.)
3. Other states, such as mental states, supervene on physical states. Give the state of the physical, there is onely one way the mental, for example, can be. Somethings this is called the supervenience and determination thesis. The idea is thatthe state of the supervening state is guaranteed by the state of the supervenience base. Thus it might be argued that biological states supervene on physicals tates. Imaginae a scenario in which a mountain lion kills and eats a deer. Even though "mountain lion" and "deer" are not physical terms, nevertheless, given the physical state of the world, it cannot be false that a mountain lion is eating a deer.
Now I don't know if I need an "and there's nothing else" clause. It looks as if according to this definition all there is is the physical and what supervenes on the physical. But I don't make any "in space and time" reference in my book's definition, but I did put it on the website. The "in space and time" was put in there to explicitly allow naturalists to be Platonists about numbers.
Can a physicalist be a Platonist about, say, numbers? Keith Parsons and Theodore Drange, in their responses to me, seemed to want to opt for forms of naturalism that allow for the existence of Platonistically conceived numbers, indeed this formed that centerpiece of his response to the argument from truth. I didn't want to argue that makes them not physicalists, what I wanted to say is that whatever these Platonic entities are, they can have nothing to do with anyone's brain states unless we reject the causal closure of the physical, and therefore such theories could not help solve any problem that had anything to do with mental causation.
Now I think I'd want to say that the causal closure principle, at least as I am understanding it, rules out any kind of causal influence by anything that is not physical, even if it is God's causing the world to exist or God's setting up a pre-established harmony between the mental and the physical. That gives you a non-physical entity causing effects in the physical world, and I really did mean to rule that out.